A converse to the Lions-Stampacchia theorem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 4, pp. 810-817.

In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.

DOI : 10.1051/cocv:2008054
Classification : 47H05, 52A41, 39B82
Mots-clés : Lions-Stampacchia theorem, variational inequality, pseudo-monotone operator 
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     title = {A converse to the {Lions-Stampacchia} theorem},
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Ernst, Emil; Théra, Michel. A converse to the Lions-Stampacchia theorem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 4, pp. 810-817. doi : 10.1051/cocv:2008054. http://www.numdam.org/articles/10.1051/cocv:2008054/

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